In the known sorting machine, trays without fixed identification marks are used. After the end of the sorting operation, the mail pieces are transferred from the sorting bins of the sorting machine into the trays which are provided in buffer storage units assigned to the sorting bins, and the concluded transfer operation is acknowledged for the respective sorting bin by means of key actuation. As a result, by means of a label printer, a label with the current destination address is printed out in coded and/or readable form for this sorting bin or with an identification label and is attached to the container by the operator. The requirement for an identification label automatically involves assignment between the identification label and the destination address, this assignment being filed in the control and being available for further identification. This solution does not allow the expedient use of trays with fixed identification marks in the mail handling process, since it is not possible for these identification marks to be coupled to the destination addresses on the basis of the abovementioned technology.